Quasi-periodic materials have been widely studied for their behavior regarding atomic dynamics, photonic, magnetic and electronic properties. They have unique properties inherited from their specific material symmetry. The recent development of additive manufacturing gives the opportunity to produce quasi-periodic structures to benefit from their unique capability. In this paper, quasi-periodic beam lattices are produced and failure experiments are performed. Then, a numerical model is proposed and validated. It is obtained that quasi-periodic Penrose lattices can outperform their periodic counterpart. These results open new ways to design architected materials with enhanced failure energy dissipation capabilities.